Probability Distribution Wiki

Introduction to probability distribution wiki:

Wikipedia has list of thousand of topics in 12 major subjects. Wiki powered by wiki software. Wiki accept content without rules. In probability theory, the probability distributions are classified in to continuous and discrete distributions. Probability distribution identifies each random variable in an experiment or with in a particular interval that is when the probability variable is continuous.  In this article we shall discuss probability distribution wiki example problem.
Probability Distribution Wiki Example Problem:

Example:

A coin is tossed 15 times, when tossing the coin find the probability of getting at least 8 tails solve by using binomial distribution.

Solution:

Step 1:

Given,

Number of total trials n = 15

Number of total success (getting tails) r = 8

Probability of success on any single event p = 0.5

Step 2:

To use the formula calculate nCr .

nCr = `(( n!) / ((n-r)!) ) / (r!)`

= (15! / (15-8)! ) / 8!

= (15! / 7! ) / 8!

= `((1307674368000/ 5040)) / (40320)`

= `(259459200/ 40320)`

= 6435

Step 3:

Find pr.

pr = 0.58

= 0. 00390625

Step 4:

To find the (1-p)n-r  and calculate 1-p and n-r.

1-p = 1-0.5 = 0.5

n-r = 15 – 8 = 7

Step 5:

Find the value of (1-p)n-r.

= 0.57

= 0. 0078125

Step 6:

Solving P(X = r) = nCr p r (1-p)n-r

= 6435 × 0. 00390625 × 0. 0078125

= 0.19638061.

The probability of getting exactly 8 tails is 0.196

Example:

A coin is flipping; Find the probability of flipping a coin gets the ninth head on the eleventh flipping of coin solve the problem with the help of negative binomial distribution.

Solution:

Step 1:

Number of total trials n = 11 (flipping the coin eleventh times).

Number of successes r (head as a success) = 9

Probability of success for any coin flip p = 0.5

Step 2:

Find n-1 and r-1.

n-1 = 11-1 = 10

r-1 = 9-1 = 8

Step 3:

To find n-1Cr-1 Calculate ((n-1)-(r-1))!

(n-1)-(r-1) = 10-8 = 2

((n-1)-(r-1))! = 2! = 2.

Step 4: Find (n-1)!

= 10! = 3628800

Step 5: Find (r-1)!

= 8! = 40320.

Step 6: Find `((n-1)!) / (((n-1)-(r-1))!)`

= 3628800 /2 = 1814400

Step 7: To solve n-1Cr-1 formula.

= `1814400 /40320` = 45

Step 8: Find pr.

= 0.59 = 0. 001953125

Step 9: To Find (1-p)n-r Calculate 1-p and n-r.

1-p = 1-0.5 = 0.5

n-r = 11-9 = 2

Step 10: Calculate (1-p)n-r.

= 0.52 = 0.25

Step 11: Calculate Negative Binomial Distribution.

= 45 ×0. 001953125 × 0. 25= 0.02197265625.

The probability on head for the ninth times on the eleventh coin flip is 0. 0219

 

 

Probability Distribution Wiki Practice Problem:

Problem:

A coin is flipping; Find the probability of flipping a coin gets the sixth tail on the tenth flipping of coin solve the problem with the help of negative binomial distribution.

Answer:

The probability on tail for the sixth times on the tenth coin flip is 0. 12305

Problem:

A coin is tossed 13 times, when tossing the coin find the probability of getting at least 5 tails solve by using binomial distribution.

Answer:

The probability of getting exactly 5 tails is 0.157